How to make a curve segment perpendicular to a face?
Unfortunately Blender isn't great for precision modelling as it currently stands, and it becomes even more difficult with bezier curves. That being said you can achieve most operations even if it is an involved and time consuming process.

You could try one of three methods


Enter edit mode on your mesh
Select the face you want to make the curve perpendicular to
Snap the cursor to it
Add a curve there
Enter edit mode in the curve
Make both handle types Vector
Move the starting point of the curve to local coordinate 0,0,0
Now exit edit mode of the curve and enter edit mode in the mesh
Extrude previously selected face (this is a temporary hack)
Now snap the cursor to the newly created face
You can now undo the extrusion and exit edit mode
Enter edit mode on the previously created curve and snap the end point to the cursor
Profit!


The con of this method is the curve's axis wont be properly oriented to be perpendicular to the face, only the segment, so you couldn't easily convert it to a bi dimensional 2D curve (if that is what you want).
Also it can be time consuming and become unpractical for many iterations.



This second method is my favorite and as the advantage to leave your curve properly oriented, however it can become inadequate if you only want a few instances.


Snap the cursor to the object whose face you want to make the curve perpendicular to (not the single face)
Add a curve there
Enter edit mode and make it's vertex start at 0,0,0 and end at 0,0,1
Now exit edit mode and parent the curve to the mesh
Select the mesh object and in the Properties Window > Object > Duplication > Enable Face duplication
Now make the curves independent objects with the operator "Make Duplicates Real*
Profit!




Third method is the simplest using snapping, but may give inaccurate results because Blender may average the normals of surrounding vertex


Turn on "Align the rotation with the snapping target" option at the bottom of the 3D view right next to the snap options
Switch to  "Snap to Faces" mode
Add a new curve
Move it with G and use snapping to align it to the surface normal as you move it around by pressing Ctrl while grabbing.
If you turn on "Project individual elements on the surface of other objects" option (also next to the snap options), the curve will orient itself to the surface (no need for pressing Ctrl).  
Enter edit mode in the curve
Translate one curve endpoint to the face  
Switch to  "Snap to Vertex" mode
Translate handle point (or second point for Nurbs) to the point from step 6  
Translate the same point along the Z axis to get a perpendicular start/segment  
Grand Total profit!